Enhancing cavity cooling with cavity driving

Cavity-mediated cooling has the potential to become one of the most efficient techniques to cool molecular species down to very low temperatures. In this paper we analyse cavity cooling with single-laser driving for relatively large cavity decay rates κ and relatively large phonon frequencies ν. It is shown that cavity cooling and ordinary laser cooling are essentially the same within the validity range of the Lamb–Dicke approximation. This is done by deriving a closed set of rate equations and calculating the corresponding stationary state phonon number and cooling rate. For example, when ν is either much larger or much smaller than κ, the minimum stationary state phonon number scales as κ2/16ν2 (strong confinement regime) and as κ/4ν (weak confinement regime), respectively.Cavity-mediated cooling has the potential to become one of the most efficient techniques to cool molecular species down to very low temperatures. In this paper we analyse cavity cooling with single-laser driving for relatively large cavity decay rates κ and relatively large phonon frequencies ν. It is shown that cavity cooling and ordinary laser cooling are essentially the same within the validity range of the Lamb–Dicke approximation. This is done by deriving a closed set of rate equations and calculating the corresponding stationary state phonon number and cooling rate. For example, when ν is either much larger or much smaller than κ, the minimum stationary state phonon number scales as κ2/16ν2 (strong confinement regime) and as κ/4ν (weak confinement regime), respectively.

arXiv:1006.3008Journal of Modern OpticsJan 22, 201112 citations

A quantum approach to cavity mediated laser cooling

Tony Blake

Cavity-mediated cooling has the potential to become one of the most efficient techniques to cool molecular species down to very low temperatures. This thesis studies the use of rate equations to analyse the cooling process in such systems. In particular the master equation is used to find rate equations that can determine the rate of change of phonons in the system. The general idea behind cavity cooling is the continuous conversion of phonons into cavity photons. While there is no spontaneous emission and decay rate associated with the concept of phonons, photons are created after a change in the phonon number has occurred and can then leak out through the cavity mirrors easily. Hence the conversion of phonons into photons can result in the constant removal of phonon energy from the system. In this thesis we compare cavity mediated cooling with single particle laser cooling. It is shown that cavity cooling is essentially the same as ordinary laser cooling. This is done by calculating the stationary state phonon number mss and the cooling rate y as a function of the system parameters. For example, when the trap phonon frequency υ is either much larger or much smaller than the cavity decay rate k , the minimum stationary state phonon number scales as k²/16v² (strong confinement regime) and as k/4 (weak confinement regime), respectively. Replacing k with Ѓ yields the steady states associated with ordinary laser cooling.Cavity-mediated cooling has the potential to become one of the most efficient techniques to cool molecular species down to very low temperatures. This thesis studies the use of rate equations to analyse the cooling process in such systems. In particular the master equation is used to find rate equations that can determine the rate of change of phonons in the system. The general idea behind cavity cooling is the continuous conversion of phonons into cavity photons. While there is no spontaneous emission and decay rate associated with the concept of phonons, photons are created after a change in the phonon number has occurred and can then leak out through the cavity mirrors easily. Hence the conversion of phonons into photons can result in the constant removal of phonon energy from the system. In this thesis we compare cavity mediated cooling with single particle laser cooling. It is shown that cavity cooling is essentially the same as ordinary laser cooling. This is done by calculating the stationary state phonon number mss and the cooling rate y as a function of the system parameters. For example, when the trap phonon frequency υ is either much larger or much smaller than the cavity decay rate k , the minimum stationary state phonon number scales as k²/16v² (strong confinement regime) and as k/4 (weak confinement regime), respectively. Replacing k with Ѓ yields the steady states associated with ordinary laser cooling.

Sep 1, 20110 citations

Rate-equation approach to cavity-mediated laser cooling

Tony Blake, Andreas Kurcz, Almut Beige

The cooling rate for cavity-mediated laser cooling scales as the Lamb-Dicke parameter $\ensuremath{\eta}$ squared. A proper analysis of the cooling process hence needs to take terms up to ${\ensuremath{\eta}}^{2}$ in the system dynamics into account. In this paper, we present such an analysis for a standard scenario of cavity-mediated laser cooling with $\ensuremath{\eta}\ensuremath{\ll}1$. Our results confirm that there are many similarities between ordinary and cavity-mediated laser cooling. However, for a weakly confined particle inside a strongly coupled cavity, which is the most interesting case for the cooling of molecules, numerical results indicate that more detailed calculations are needed to model the cooling process accurately.The cooling rate for cavity-mediated laser cooling scales as the Lamb-Dicke parameter $\ensuremath{\eta}$ squared. A proper analysis of the cooling process hence needs to take terms up to ${\ensuremath{\eta}}^{2}$ in the system dynamics into account. In this paper, we present such an analysis for a standard scenario of cavity-mediated laser cooling with $\ensuremath{\eta}\ensuremath{\ll}1$. Our results confirm that there are many similarities between ordinary and cavity-mediated laser cooling. However, for a weakly confined particle inside a strongly coupled cavity, which is the most interesting case for the cooling of molecules, numerical results indicate that more detailed calculations are needed to model the cooling process accurately.

arXiv:1202.2992Physical Review AJul 23, 20127 citations

Laser cooling a trapped atom in a cavity: Bad-cavity limit

J. I. Cirac, Maciej Lewenstein, P. Zoller

We analyze theoretically a one-dimensional model of laser cooling of an atom or ion trapped in a cavity. We assume that the cavity loss rate is much larger than the atom-cavity coupling (bad-cavity limit) and that the atomic excited state is weakly occupied (low saturation limit). After elimination of the cavity mode and the atomic excited state, we derive rate equations for the populations of the trap states. We find that in the Lamb-Dicke limit the atom can be cooled to the ground state of the trap even in the strong confinement limit. This result is interpreted in terms of quantum interferences between different cooling and heating processes involving spontaneous emission in the cavity.We analyze theoretically a one-dimensional model of laser cooling of an atom or ion trapped in a cavity. We assume that the cavity loss rate is much larger than the atom-cavity coupling (bad-cavity limit) and that the atomic excited state is weakly occupied (low saturation limit). After elimination of the cavity mode and the atomic excited state, we derive rate equations for the populations of the trap states. We find that in the Lamb-Dicke limit the atom can be cooled to the ground state of the trap even in the strong confinement limit. This result is interpreted in terms of quantum interferences between different cooling and heating processes involving spontaneous emission in the cavity.

Physical Review AFeb 1, 199560 citations

Ground-state laser cooling beyond the Lamb-Dicke limit

Giovanna Morigi, J. I. Cirac, Maciej Lewenstein +1 more

We propose a laser cooling scheme that allows to cool a single atom confined in a harmonic potential to the trap ground state $|0>$ . The scheme assumes strong confinement, where the oscillation frequency in the trap is larger than the effective spontaneous decay width, but is not restricted to the Lamb-Dicke limit, i.e. the size of the trap ground state can be larger than the optical wavelength. This cooling scheme may be useful in the context of quantum computations with ions and Bose-Einstein condensation.We propose a laser cooling scheme that allows to cool a single atom confined in a harmonic potential to the trap ground state $|0>$. The scheme assumes strong confinement, where the oscillation frequency in the trap is larger than the effective spontaneous decay width, but is not restricted to the Lamb-Dicke limit, i.e. the size of the trap ground state can be larger than the optical wavelength. This cooling scheme may be useful in the context of quantum computations with ions and Bose-Einstein condensation.

arXiv:quant-ph/9706017Europhysics Letters (EPL)Jul 1, 199742 citations

Sub-Doppler cavity cooling beyond the Lamb-Dicke regime

Boon Leng Chuah, Nicholas C. Lewty, Radu Cazan +1 more

We investigate the dynamics of cavity cooling of a single ion beyond the Lamb-Dicke regime and demonstrate a cooling limit of approximately 50 $%$ of the Doppler temperature using a high finesse cavity. We also study the statistical properties of the ion-cavity emission and present a model that maps the phonon states to the photon states. With this model, we explain the super-Poissonian photon distribution observed in our experiments and propose a method to estimate the ion temperature in a real-time manner based on the statistical behavior of the photon emission from the cavity.We investigate the dynamics of cavity cooling of a single ion beyond the Lamb-Dicke regime and demonstrate a cooling limit of approximately 50$%$ of the Doppler temperature using a high finesse cavity. We also study the statistical properties of the ion-cavity emission and present a model that maps the phonon states to the photon states. With this model, we explain the super-Poissonian photon distribution observed in our experiments and propose a method to estimate the ion temperature in a real-time manner based on the statistical behavior of the photon emission from the cavity.

arXiv:1302.4613Physical Review AApr 18, 20137 citations

We propose a laser cooling scheme that allows to cool a single atom confined in a harmonic potential to the trap ground state

|0>

. The scheme assumes strong confinement, where the oscillation frequency in the trap is larger than the effective spontaneous decay width, but is not restricted to the Lamb-Dicke limit, i.e. the size of the trap ground state can be larger than the optical wavelength. This cooling scheme may be useful in the context of quantum computations with ions and Bose-Einstein condensation.

We investigate the dynamics of cavity cooling of a single ion beyond the Lamb-Dicke regime and demonstrate a cooling limit of approximately 50

%

of the Doppler temperature using a high finesse cavity. We also study the statistical properties of the ion-cavity emission and present a model that maps the phonon states to the photon states. With this model, we explain the super-Poissonian photon distribution observed in our experiments and propose a method to estimate the ion temperature in a real-time manner based on the statistical behavior of the photon emission from the cavity.